Techniques for iterative reduction of uncertainty in water distribution networks

ABSTRACT

In one aspect, a method for reducing uncertainty in a hydraulic model of a water distribution network due to uncertain parameters and faults in the water distribution network is provided which includes the steps of: (i) calculating an optimized placement of sensors throughout a given uncertain section of the water distribution network; (ii) collecting data from the sensors; (iii) partitioning the given uncertain section of the water distribution network into observable and unobservable sub-sections based on the hydraulic model and a) a position, b) a number, and/or c) a type of the sensors that are available; (iv) correcting uncertain parameters and identifying faults for each of the observable sub-sections; (v) calculating a global uncertainty value for each of the unobservable sub-sections; and (vi) repeating the steps (i)-(vi) iteratively, at each iteration selecting an uncertain sub-section of the water distribution network, until no uncertain sub-sections of the water distribution network remain.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/709,483 filed on Dec. 10, 2012, now U.S. Pat. No. 9,582,775, thecontents of which are incorporated by reference as if fully set forthherein.

FIELD OF THE INVENTION

The present invention relates to analysis of water distribution networks(WDNs) and more particularly, to techniques for iteratively reducinguncertainty in WDN models.

BACKGROUND OF THE INVENTION

Simulation models of water distribution networks (WDNs) are fundamentalfor management, operational and monitoring purposes. Typical usage ofthe models range from pumps scheduling, management of the pressures atthe nodes of the network, identification of faults (e.g., leaks),monitoring of water quality, etc.

WDN models available to utility companies, however, are often inaccuratedue to the imperfect representation of the complete physical process andthe incomplete knowledge of all of the required parameters. Theuncertainty in the models is typically reduced with the calibration,where the parameters are adjusted such that pressures and flowspredicted by the model match a set of actual observed field data to somedesirable or acceptable level. Many methods have been proposed for thesolution of the calibration problem. Methods for the optimal placementof sensors around the network have also been studied, in order tomaximize the sensitivity of certain desired parameters to the collecteddata and therefore improve the quality of the estimation.

A major issue with the reduction of uncertainty in WDN models is thescarcity of measurement points around the network, with the number ofparameters to be adjusted usually being much larger than the availablemeasurements. Calibration can therefore only be successful on a selectedsubset of parameters of the model, which usually leaves significantuncertainty in major areas of the WDN model. Another issue, also relatedto the poor availability of measurement points, is the exactlocalization of the source of uncertainty. In some situations, in fact,an inconsistency between model predictions and field measurements couldambiguously be related to a number of different parameters or to a fault(e.g., leaks) in the network, the problem of exactly inferring thesource of uncertainty could be undetermined with the availablemeasurements.

Therefore, improved techniques for reducing uncertainty in WDN modelsthat solves the problem of having scarce measurement points around thenetwork would be desirable.

SUMMARY OF THE INVENTION

The present invention provides techniques for analysis of waterdistribution networks (WDNs). In one aspect of the invention, a methodfor reducing uncertainty in a hydraulic model of a water distributionnetwork due to uncertain parameters and faults in the water distributionnetwork is provided. The method includes the steps of: (i) calculatingan optimized placement of sensors throughout a given uncertain sectionof the water distribution network; (ii) collecting data from thesensors; (iii) partitioning the given uncertain section of the waterdistribution network into observable and unobservable sub-sections basedon the hydraulic model and one or more of a) a position, b) a number,and c) a type of the sensors that are available; (iv) correctinguncertain parameters and identifying faults for each of the observablesub-sections; (v) calculating a global uncertainty value for each of theunobservable sub-sections; and (vi) repeating the steps (i)-(vi)iteratively, at each iteration selecting an uncertain sub-section of thewater distribution network, until no uncertain sub-sections of the waterdistribution network remain.

In another aspect of the invention, a system for reducing uncertainty ina hydraulic model of a water distribution network due to uncertainparameters and faults in the water distribution network is provided. Thesystem includes a sensor placement module configured to calculate anoptimized placement of sensors throughout a given uncertain section ofthe water distribution network; a diagnosis and calibration moduleconfigured to (a) partition the given uncertain section of the waterdistribution network into observable and unobservable sub-sections basedon the hydraulic model and one or more of a position, a number, and atype of the sensors that are available, (b) correct uncertain parametersand identify faults for each of the observable sub-sections, and (c)calculate a global uncertainty value for each of the unobservablesub-sections.

A more complete understanding of the present invention, as well asfurther features and advantages of the present invention, will beobtained by reference to the following detailed description anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating an exemplary system forperforming the present iterative process for reducing uncertainty in awater distribution network (WDN) model according to an embodiment of thepresent invention;

FIG. 2 is a diagram illustrating exemplary methodology for iterativelyreducing uncertainty in a WDN model according to an embodiment of thepresent invention; and

FIG. 3 is a diagram illustrating an exemplary apparatus for performingone or more of the methodologies presented herein according to anembodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Provided herein are techniques for the iterative reduction ofuncertainty in water distribution networks, which are able to overcomethe practical difficulty of poor availability of field measurementpoints and faults (e.g., leaks, malfunctioning valves or pumps) acrossthe network. As will be described in detail below, at each iteration,focus is put on uncertain sub-sections of the network, where the presentmethod calculates the optimal measurement points and conditions giventhe number of available sensors. The present method then automaticallypartitions the network into observable and unobservable sub-sections.For each observable sub-section the uncertain parameters/faults (i.e.,parameter errors and network faults) are identified (localized) and theparameter errors are corrected, while a coarse uncertainty estimationfor the unobservable sub-sections is produced—which indicates thatfurther exploration is required. At the next iteration, focus is movedto one of the uncertain sub-sections.

With regard to the distinction between parameter errors and networkfaults, the idea is that the uncertainty that we try to localize maycome from two main sources: model uncertainties (e.g., wrong orincorrect parameters of the hydraulic model, like pipe roughness) orreal process faults (e.g., the presence of a leak, a valve or a pump notfunctioning properly). The present techniques can ultimately identifyboth sources of uncertainty. However, calibration (see below) can onlycorrect the model with respect to the former (modeler parametricuncertainties), while the latter can only be corrected by physicalintervention on the field.

An uncertain sub-section is a collection of network nodes (apart/section of the network) and connecting pipes where a mismatch isexperienced between sensor measurements and model predictions. At thefirst iteration of the process (initialization) the uncertainsub-section is the whole network. At each subsequent iteration, thesystem then separates the part of the network being analyzed intosub-sections for which a global uncertainty measure is calculated. Atthe next iteration the user chooses to focus the analysis on one ofthese sub-sections.

Specifically, each iteration of the method consists of an analysis ofone “section” of the network and produces an output consisting of“sub-sections” of the network. Each of the output “sub-sections” canbecome the “section” analyzed in the following iteration(s), which coulditeratively separate it further into smaller “sub-sections.” The idea isthat when an iteration is being described, the section is the part ofthe network under analysis and the sub-sections are the output of theiteration.

With regard to uncertain/observable/non-observable sub-sections, eachiteration of the method, by analyzing a section of the network,partitions the section into sub-sections. Some of the sub-sections areobservable and a full diagnosis/localization is provided, so thesesub-sections are not uncertain anymore (all anomalies, if present, havebeen identified). Some of the sub-sections are non-observable and only ameasure of the level of uncertainty in those sub-sections is presented.

Based on this, the “uncertain sub-sections” are non-observable sections,for which the iteration produced a global measure of the uncertainty(how much these sub-sections seem to contain some source of anomaly).So, based on the above, these are candidate sub-sections to be exploredand analyzed at the next iteration.

The “uncertain sub-section” (i.e., one of the candidate sub-sections)selected for the next iteration, is one of the “non-observablesub-sections” for which a global measure of uncertainty has beenproduced. In fact, although the user knows now that these sections are“uncertain” and by how much, he/she knows that there is something wrongthere, but the user does not know what, and needs to further explorethat area of the network.

The user of the system, at each iteration, can choose a part of thenetwork (section) to analyze. Usually, unless the user already knowsabout a specific part of the network containing uncertainties oranomalies (based on some external source of information), he/she willchoose the whole network at a first iteration, but not necessarily.Then, as a result of the iteration, the method would produce sub-parts(sub-sections) of the section under analysis (this could be the wholenetwork at the first iteration). Based on this output and the globalmeasure of uncertainty assigned by the method to each sub-section of thenetwork the user selects which of these sub-sections the method shouldanalyze in the next iteration.

Observable sub-sections indicate a part (group of nodes/pipes) of thenetwork where enough sensor data are available such that it is possibleto clearly identify the source of uncertainty (parameters or faults).The uncertainty identification can be done using classical residualanalysis (difference between measurements and model predictions). Onceidentified, the uncertain parameters can be corrected with known modelidentification or calibration techniques. By way of example only, see M.Cisty et al., “Automated Calibration of Irrigation Projects SimulationModel by Harmony Search Optimization,” International Symposium on WaterManagement and Hydraulic Engineering, Ohrid/Macedonia, 1-5 Sep. 2009,the contents of which are incorporated by reference herein. Theuncertain faults are not corrected (they are physical problems, whichare identified and the user is simply acknowledged about them—seeabove).

In the case where the number of available sensors is too small to haveany meaningful diagnosis, an automatic method is provided herein forsensor placement where multiple sets of measurements are collected atdifferent points of the network and at different times within oneiteration of the method described above. The different sets ofmeasurements are then properly integrated in the diagnosis/correctionstep of the method above.

By “meaningful diagnosis” it is meant that in some particular cases thenumber of available sensors and their position in the network is notgood enough to successfully separate the network into sub-sections andproduce a measure of the uncertainty for each one of them. In thesecases multiple measurement collection iterations (where the fewavailable sensors are moved at different points at each iteration) arerequired before a single diagnosis step is performed.

While conventional methods for the calibration of water distributionnetworks only allow for the calibration/estimation of a selected andnon-complete sub-set of the uncertain parameters, the present methodallows for the correct localization and correction of the uncertaintyover a water distribution network, without the need for limiting thediagnosis to a number of parameters. The present method itself guidesthe user through the iterations for the exploration of the networkmodel, progressively indicating where the uncertainty is and producingless uncertain estimates.

The details of the present techniques will now be described by way ofreference to the following non-limiting embodiments. FIG. 1 is aschematic diagram illustrating an exemplary system 100 for performingthe present iterative process for reducing uncertainty in a waterdistribution network (WDN) model. System 100 may be embodied in anapparatus, such as apparatus 300 shown in FIG. 3, described below.

According to an exemplary embodiment, system 100 is a software programthat includes two main components. As shown in FIG. 1, these componentsinclude (but are not limited to) i) a sensor placement module 102, andii) a diagnosis/calibration module 104. The interaction of thecomponents with each other and (optionally) with a user (via a userinterface—not shown) provides a solution to the reduction of uncertaintyin the model of a water distribution network (WDN). See below. Ahydraulic model consisting of the connectivity and the parameters ofnodes and pipes is needed for the process. This model is utilized bothby the sensor placement module and by the diagnosis/calibration module.The hydraulic model is an input provided to the user at the start of themethod (initialization). This is typically available from networkoperators in the form of set of nodes/links, their parameters and theirconnectivity graph, usually in electronic format (text or binary file).

FIG. 2 is a diagram illustrating exemplary methodology 200 foriteratively reducing uncertainty in a WDN model according to the presenttechniques. In step 202, a user initializes the process with a desirednetwork (or section of the network). As provided above, in a firstiteration (an initialization) the whole network may constitute the“uncertain sub-section” chosen. In step 202 the user can (optionally)also set some prior knowledge about the uncertainty of parameters, ifthis information is available to the user. This information can include,but is not limited to, certainty/uncertainty information about pipeparameters (roughness, diameter), nodes demand, valve operationalstatus, etc. The uncertainty can be expressed as a typical valueinterval (e.g., the pipe diameter belongs to the interval 9-12 inches)or as mean and standard deviation (e.g., the pipe diameter is 9±2inches). By way of example only, the pipe roughness may be calculatedaccording to the techniques presented in S. Shu et al., “ModifiedMethods on Testing Roughness Coefficient of Water Pipes In Urban WaterDistribution Network,” ICPTT 2009: Advances and Experiences withPipelines and Trenchless Technology for Water, Sewer, Gas, and OilApplications, Shanghai, China (Oct. 18-21, 2009) (hereinafter “Shu”),the contents of which are incorporated by reference herein. While inpractice the value of all parameters is available and can be provided,Shu makes the point that some of them (roughness in this case) are notknown exactly and an uncertainty around them may be calculated. Valveoperational status may be evaluated by the techniques described in F. B.Prinz et al. “Automatic Monitoring of Valve Status,” Report to the U.S.Department of Energy Deputy Assistant Secretary for Breeder ReactorPrograms Washington, D.C. 20545 (January, 1988), the contents of whichare incorporated by reference herein. The user then inputs the positionof fixed measurement points in the network and the number (and type) ofavailable sensors that can be freely placed throughout the network. Thefixed measurement points are the available sensors whose position in thenetwork is fixed and cannot be changed, at least not without bigeffort/cost. The user knows their position from design information ofthe water network. The present method provides optimal positioning forthe sensors that the user is willing to move (not fixed), that is whysuch information is required as input. The term “user” here refersgenerically to one or more human users of the present system. Thus“user” as provided herein may refer to more than one person.

The first iteration of methodology 100 is then started in step 204 byautomatically calculating the optimal placement of the (both number ofsensors and types of sensors) sensors throughout the network, such thatthe diagnosis/calibration that follows (see below) can be mosteffective. By way of reference to system 100 of FIG. 1 described above,this step of calculating the optimal placement of the sensors may beperformed by the sensor placement module. The required position of thesensors, as well as an indication of a minimum time-window for theobservations (also calculated, for example, by the sensor placementmodule), is output to the user and field data are collected accordinglyvia the sensors. The optimal time window is as long as possible andhence why a minimal time-window is specified. The optimal time windowcould be calculated based on the required statistical significance ofthe diagnosis/correction method (e.g., accurate with 95% probability)and it is related to the number of measurement points, to the number ofuncertain parameters and to the statistical assumptions of theuncertainty. In the case that the available number of sensors specifiedby the user is not enough to produce a meaningful diagnosis (see steps210-212), this step also provides an optimal positioning for anadditional minimum number of sensors that would be required. In thelatter case, the measurements collection steps described in thefollowing (steps 206-208) would require multiple iterations before thediagnosis.

By way of example only, the sensors that might be employed in a WDNinclude, but are not limited to, hydraulic sensors such as waterpressure sensors, water flow sensors. Other types of sensors that mightbe employed include, but are not limited to, water temperature sensors,water quality sensors, etc. Each of these types of sensors iscommercially available. These sensors are however expensive and thuseach type of sensor cannot be implemented at every conceivable positionof interest in the WDN. Thus, the present placement optimization isneeded. As highlighted above, it is assumed herein that some sensorsavailable can be freely placed throughout the WDN (i.e., it is possiblethat some of the sensors are fixed and cannot be moved—for these fixedsensors the present process does not provide optimal placement).

Optimization of the placement of the available sensors may be carriedout using any suitable optimization process. Sensor placementoptimization is described in detail below.

In step 206, the field measurements collected (via the sensors—i.e.,sensor data) are obtained. Although the optimal-placement (for obviousreasons) does not provide positioning for fixed sensors, data from thefixed sensors (as well as data from the optimally placed sensors) arestill considered by the present method, because it is valuableinformation. Measurement collection, therefore is from “all” availablesensors, fixed and movable, where the latter have been moved to thelocation indicated by the sensor-placement module.

According to an exemplary embodiment, the sensor data is obtained fromthe user who enters the field observed data. Alternatively, the sensorsemployed can be configured to (e.g., either through a wired connectionor wirelessly) automatically transmit the data collected to an apparatus(such as apparatus 300 of FIG. 3) that is performing methodology 200.The field data collected may include, for example, hydraulic data suchas pressures and flows at one or more nodes of the network. A node in aWDN is simply the end of a pipe in the network.

Along with the data, the user may also enter information for thehydraulic model including, but not limited to, the demand conditions(e.g., relating to the time of day when data was collected from a givennode, and the typical demand profiles at the different nodes of thenetwork) and the operating conditions of the active components of thenetwork, such as storage tank levels, pressure control valve settingsand pump operation speeds. If the sensor data is automatically obtainedas provided above (instead of requiring the user to enter sensor data)then a user interface may still be provided for the user to enter thissupporting data.

In step 208 a determination is made as to whether enough fieldmeasurements have been made. This is in the case that the optimal sensorplacement in step 204 produced the optimal position of more sensors thanare available, because otherwise the following diagnosis step would notbe able to separate the network into sub-sections. In this situation theuser would have to use some of the sensors to collect measurements atmore than one point of the network over different time windows. Ifenough data has been collected (i.e., in order to perform the diagnosisand calibration steps described below), then the process continues atstep 210. However, if it is determined in step 208 that more data isneeded, then step 206 is repeated to obtain more field measurements(e.g., after one or more of the sensors have been moved) and anevaluation is again made to as to whether the data is sufficient. By wayof example only, as provided above, the field data may include hydraulicdata such as pressures and flows at one or more nodes of the networkcollected at a certain time-window. To obtain more data, the user canmove one or more of the (non-fixed) sensors to another point and collectdata (although it will be over a different time window).

In step 210, based on the hydraulic model of the network and on theavailable measurements (obtained in step 206), the section of thenetwork currently under study is separated into observable andnon-observable sub-sections. According to an exemplary embodiment, step210 is performed based on a network observability analysis. See, forexample, A. Bargiela, “An algorithm for observability determination inwater-system state estimation,” IEE Proceedings, Vol. 132, Pt. D, No. 6,November, 1985 (hereinafter “Bargiela”), the contents of which areincorporated by reference herein. For example, in Bargiela, the sectionin g of the network is partitioned into observable and non-observablesections based simply on the model and position of the availablesensors. Specifically, the method in Bargiela is based on graph theory,where the connectivity graph of the hydraulic model is partitionediteratively based on whether or not each node has a sensor and of whattype. That, or any other suitable partitioning method may be used inaccordance with the present techniques.

In step 212, based on the field data collected, the method thenautomatically runs a diagnosis/calibration module (see system 100 ofFIG. 1, described above). By diagnosis it is meant herein that anuncertainty in the model is estimated, and through calibration theuncertainty is reduced. As will be described in detail below, the“diagnosis” involves calculating uncertainty for both observable andnon-observable sub-sections of the network. For sources of uncertaintyin the observable sub-sections, the uncertainty is localized, whichmeans the source and position of the uncertainty is identified. In thecase where the uncertainty lies in the hydraulic model (for examplewrong pipe roughness), the calibration module corrects it, otherwise ifthe uncertainty is due to a process anomaly (e.g., a leak, valvemalfunctioning, etc.) the system simply flags it to the user. Namely, asdescribed above, the uncertainty reduction through calibration is onlydone when it is due to a wrong model parameter, while the source of theuncertainty is simply flagged when it is due to a process fault, wherecorrection can only be done with physical intervention on the system.Calibration of water distribution model is described generally in M.Cisty et al., “Automated Calibration of Irrigation Projects SimulationModel by Harmony Search Optimization,” International Symposium on WaterManagement and Hydraulic Engineering, Ohrid/Macedonia, 1-5 Sep. 2009(hereinafter “Cisty”), the contents of which are incorporated byreference herein. In Cisty, the calibration of a water distributionmodel is described as the process of comparing pressures and flowspredicted with observed pressures and flows for known operatingconditions, such as pump operation, tank level, pressure-reducing valvesettings, and adjusting the input model for the data to improve theagreement between the observed and predicted values.

At this stage, the method returns results to the user, where the resultsare identified parameters and faults for observable sections, anduncertainty value for non-observable sections. See FIG. 2. Ashighlighted above, for each non-observable sub-section, a globaluncertainty value is calculated and provided to the user, whichindicates how uncertain that region is, but that further exploration(e.g., with more sensors) is required in order to locate and estimatethe source of uncertainty. One way to estimate the level of uncertaintyin a non-observable part of the network is by calculating the differencebetween sensor measurements in the network section and predictions fromthe hydraulic model. Statistical testing can be applied to thisdifference value in order to improve its significance by assigning aconfidence value as well (e.g., the uncertainty value with a confidenceof 95%).

Step 212 is also referred to herein as a diagnosis step of themethodology. Specifically, step 212 carries out the diagnosis of eachsub-section produced by step 210 (observable and non-observable).

For each observable sub-section, the source of uncertainty, wherepresent, is localized and corrected. More specifically, the methodautomatically estimates updated values for the parameters of the network(e.g., pipe roughness, diameter, nodes demand, valves operationalstatus) or indicates the presence of a fault (e.g., leak). See below.

In step 214, based on the above described diagnosis/calibration process,a determination is made as to whether there are uncertain sub-sectionsof the network remaining and whether focus should be shifted to thoseuncertain regions. By way of example only, this decision may be made bythe user based on the information obtained from the previousdiagnosis/calibration process. As shown in FIG. 2, if and when there areno further uncertain sub-sections of the network remaining then theprocess is ended.

However, when uncertain sub-sections of the network remain, the previoussteps, from the calculation of the optimal sensors placement to thecalibration and uncertainty estimation, are then repeated in aniterative fashion—beginning with the user selecting one or moresub-sections of the network. As described above, at this step the usercan also set some prior knowledge about the uncertainty of parameters(e.g., certainty/uncertainty information about pipe parameters(roughness, diameter), nodes demand, valve operational status, etc.) ifthis information is available to the user. The process is then repeatedin an iterative fashion until there are no uncertain sub-sections of thenetwork remaining.

The aspects of the above-provided method are now described in furtherdetail. The components of the present system can be implemented asfollows.

Sensors placement—Based on the number of available sensors and the modelof the network (or the sub-section of the network) on which the currentiteration of the method is focused, an optimization process provides theoptimal placement of the sensors. As provided above, optimization of theplacement of the available sensors may be carried out using any suitableoptimization process. For illustrative purposes only, by way of example,one suitable process for optimizing placement of the sensors accordingto the present techniques is described in A. Preis et al.,“Multi-objective Sensor Network Placement Model for IntegratedMonitoring of Hydraulic and Water Quality Parameters,” World City WaterForum (WCWF 2009), Incheon, Korea (August, 2009) (hereinafter “Preis”),the contents of which are incorporated by reference herein. In Preis, amethod for sensor placement is provided for drinking water utilitiesthat maximizes both contaminant event sensor detection likelihood aswell as sensor hydraulic sensitivity to variations in nodal demand.

Preferably, the optimization problem maximizes the sensitivity functionof the measured variables to the parameters of interest in the network.See for example Preis where the sensor sensitivity to variations innodal demand are maximized. The optimization can be solved by using anyexisting process for non-linear problems, such as genetic algorithms ormixed integer programming, the application of which to the sensoroptimization problem, given the instant teachings, would be apparent toone of skill in the art.

Diagnosis/Calibration—Based on the hydraulic model of the water network,a measurement model that relates the available measurements to thenetwork states is built, where the states of interest are the uncertainparameters of the network, specifically the pipes resistance (whichsummarizes all of the physical parameters of the pipes, includingdiameter, roughness, presence of leak, etc . . . ). The model islinearized around the operating point, given by the field measurementscollected by the user (the sensor readings) and by the operatingconditions provided by the user—see above. One example of operatingconditions provided by the user are the nodal demands. Knownobservability processes are run and the network is separated inobservable and non-observable sections. By way of example only, asuitable observability process for use herein is described in M. Luonget al., “Observability, Redundancy, Reliability and Integrated Design ofMeasurement Systems,” Proc of the 2^(nd) IFAC Symposium on IntelligentComponents and Instruments for Control Applications, SICICA '94 (Jun.8-10, 1994) (hereinafter “Luong”), the contents of which areincorporated by reference herein. Luong addresses the issue of sensorplacement and provides an observability algorithm that takes intoaccount measured and unmeasured variables.

Next, for each observable and non observable section, the model is usedfor elaborating a fault diagnosis strategy which operates through thedetection, the localization and the severity estimation of theuncertainty. The detection of the uncertainty might be based onresiduals calculation. The residual is an uncertainty indicator and iscomputed through the difference between the actual field measurements(i.e., data from the sensors) and the values predicted by the model. Inthe absence of uncertainties, the residual should be equal to zero andbecomes different from zero in the opposite case. For a discussion ofthe use of residuals in fault diagnosis in water distribution systemssee, for example, J. Gertler et al., “Leak Detection and Isolation inWater Distribution Networks using Principal Component Analysis andStructured Residuals,” 2010 Conference on Control and Fault-Tolerant(SysTol), pgs. 191-196 (Oct. 6-8, 2010), the contents of which areincorporated by reference herein.

The hydraulic model, by allowing one to determine the residuals, is amathematical expression linking the pressure drop between theextremities of a given pipe and the associated flow rate. Specifically,the hydraulic model can be regarded as a characterization of thephysical parameters of the pipe and this methodology is sufficientlyreliable for building model-based uncertainty estimation. In order toimprove the reliability on the decision to be made with respect to theuncertainty status of the section of the network, the computed residualscan be associated with statistical hypothesis testing. In this context,the main characteristics of the tests will be established from the meanand the variance of residuals. Hypothesis testing is commonly used inresidual analysis for anomaly detection. It consists of making anassumption about the probability distribution of the residuals in normalconditions. Then, when the residuals are calculated, they are testedagainst this assumption. The output of the test is whether the value ofthe residuals indicates normal condition (everything is okay) orabnormal behavior (something is wrong), in a statistical sense (that iswith a certain probability). In the case of abnormal behavior themagnitude of the residual also indicates the severity of the anomaly(how far from normal conditions we are).

For the non-observable sections, the outcome of the statistical test ispresented to the user, indicating whether the section containsuncertainty/faults or not. For the observable sections, the measurementsare sufficient to operate a localization of the uncertainty.

This localization is based on an analysis of the features of theresiduals, both in the time and in the frequency domain. Differentfeatures can be mapped to different sources of uncertainty, which can bea fault (e.g., a leak) or an incorrect parameter (i.e., parametricuncertainties). An incorrect parameter is a parameter of the hydraulicmodel that the diagnosis indicates to be incorrect. For example theroughness of the pipes is typically not known with accuracy. Thelocalization step in the diagnosis may indicate that one roughnesscoefficient is not what was specified in the model. The calibration stepwould then correct it.

It is notable that localization here means identification of the sourceand position of the uncertainty/anomaly. That is what causeduncertainty/anomaly (roughness parameter, pipe diameter parameter,presence of a leak, . . . ) and where it is in the network.

According to the available sensors, the residuals calculated in thediagnosis step are available at different points in space and timeacross the network. One way of performing localization is to identifyhow different sources of uncertainty produce different patterns in thespatio-temporal collection of residuals. For example, based on the modelsensitivity analysis, one could build a classification model that, giventhe pattern in the residual, outputs what is the most probable causethat produced it. Such a classifier can be built using the hydraulicmodel and simulating the different types of uncertainties/faults thatcan appear in the network. See, for example, R. Perez et al., “LeakageIsolation using Pressure Sensitivity Analysis in Water DistributionNetworks: Application to the Barcelona case study,” Proceedings of the12th IFAC Symposium on Large Scale Systems: Theory and Applications(2010), France, Volume 9, Part 1, the contents of which are incorporatedby reference herein.

After localization, parametric uncertainties are corrected by updatingthe model such that the residual is zero. This can be done withnon-linear optimization methods, where the residual is minimized such asfor example a Gauss-Newton method that minimizes a weighted sum of thesquared residuals. If the uncertainty is due to the presence of a leak,the position of the leak is estimated from analysis of the residuals andknowledge of the hydraulic model.

Turning now to FIG. 3, a block diagram is shown of an apparatus 300 forimplementing one or more of the methodologies presented herein. By wayof example only, apparatus 300 can be configured to implement one ormore of the steps of methodology 200 of FIG. 2 for reducing uncertaintyin a hydraulic model of a water distribution network due to uncertainparameters and faults in the water distribution network.

Apparatus 300 includes a computer system 310 and removable media 350.Computer system 310 includes a processor device 320, a network interface325, a memory 330, a media interface 335 and an optional display 340.Network interface 325 allows computer system 310 to connect to anetwork, while media interface 335 allows computer system 310 tointeract with media, such as a hard drive or removable media 350.

As is known in the art, the methods and apparatus discussed herein maybe distributed as an article of manufacture that itself comprises amachine-readable medium containing one or more programs which whenexecuted implement embodiments of the present invention. For instance,when apparatus 300 is configured to implement one or more of the stepsof methodology 200 the machine-readable medium may contain a programconfigured to (i) calculate an optimized placement of sensors throughouta given uncertain section of the water distribution network; (ii)collect data from the sensors; (iii) partition the given uncertainsection of the water distribution network into observable andunobservable sub-sections based on the hydraulic model and one or moreof a) a position, b) a number, and c) a type of the sensors that areavailable; (iv) correct uncertain parameters and identify faults foreach of the observable sub-sections; (v) calculate a global uncertaintyvalue for each of the unobservable sub-sections; and (vi) repeat thesteps (i)-(vi) iteratively, at each iteration selecting an uncertainsub-section of the water distribution network, until no uncertainsub-sections of the water distribution network remain.

The machine-readable medium may be a recordable medium (e.g., floppydisks, hard drive, optical disks such as removable media 350, or memorycards) or may be a transmission medium (e.g., a network comprisingfiber-optics, the world-wide web, cables, or a wireless channel usingtime-division multiple access, code-division multiple access, or otherradio-frequency channel). Any medium known or developed that can storeinformation suitable for use with a computer system may be used.

Processor device 320 can be configured to implement the methods, steps,and functions disclosed herein. The memory 330 could be distributed orlocal and the processor device 320 could be distributed or singular. Thememory 330 could be implemented as an electrical, magnetic or opticalmemory, or any combination of these or other types of storage devices.Moreover, the term “memory” should be construed broadly enough toencompass any information able to be read from, or written to, anaddress in the addressable space accessed by processor device 320. Withthis definition, information on a network, accessible through networkinterface 325, is still within memory 330 because the processor device320 can retrieve the information from the network. It should be notedthat each distributed processor that makes up processor device 320generally contains its own addressable memory space. It should also benoted that some or all of computer system 310 can be incorporated intoan application-specific or general-use integrated circuit.

Optional display 340 is any type of display suitable for interactingwith a human user of apparatus 300. Generally, display 340 is a computermonitor or other similar display.

Although illustrative embodiments of the present invention have beendescribed herein, it is to be understood that the invention is notlimited to those precise embodiments, and that various other changes andmodifications may be made by one skilled in the art without departingfrom the scope of the invention.

What is claimed is:
 1. A system for reducing uncertainty in a hydraulicmodel of a water distribution network due to uncertain parameters andfaults in the water distribution network, the system comprising aprocessor device, coupled to a memory, that implements: a sensorplacement module configured to calculate an optimized placement ofsensors throughout a given uncertain section of the water distributionnetwork; and a diagnosis and calibration module configured to (a)partition the given uncertain section of the water distribution networkinto observable and unobservable sub-sections based on the hydraulicmodel, and one or more of a position, a number, and a type of thesensors that are available, (b) correct uncertain parameters andidentify faults for each of the observable sub-sections, (c) calculate aglobal uncertainty value for each of the unobservable sub-sections, and(d) repeat (a)-(d) iteratively, at each iteration selecting an uncertainsub-section of the water distribution network, thereby iterativelyreducing the uncertainty until no uncertain sub-sections of the waterdistribution network remain, wherein during a first iteration the waterdistribution network as a whole is selected for analysis, and at eachsubsequent iteration sub-sections of the water distribution network areselected for analysis.
 2. The system of claim 1, wherein the faults inthe water distribution network comprise leaks.
 3. The system of claim 1,wherein the optimized placement of the sensors throughout the waterdistribution network is calculated based on a number of sensorsavailable and types of sensors available.
 4. The system of claim 1,wherein one or more of the sensors comprise hydraulic sensors.
 5. Thesystem of claim 4, wherein the hydraulic sensors are selected from thegroup consisting of: water pressure sensors and water flow sensors. 6.The system of claim 1, wherein one or more of the sensors are selectedfrom the group consisting of: water temperature sensors and waterquality sensors.
 7. The system of claim 1, wherein the sensors compriseboth fixed location sensors and movable sensors.
 8. The system of claim7, wherein the sensor placement module is configured to direct movementof the movable sensors to locations indicated by the optimized placementuntil a sensor has been placed and data has been collected from all ofthe locations indicated by the optimized placement.
 9. The system ofclaim 8, wherein data is collected from the locations indicated by theoptimized placement at different time windows.
 10. The system of claim1, wherein the position, the number, and the type of the sensors thatare available are obtained from a user.
 11. The system of claim 1,wherein data from the sensors is obtained from a user who manuallyenters the data into the system.
 12. The system of claim 1, wherein datafrom the sensors is automatically transmitted to the system by thesensors.
 13. The system of claim 1, wherein the uncertain parameterscomprise pipe roughness.
 14. The system of claim 1, wherein thediagnosis and calibration module is further configured to identify thefaults for each of the observable sub-sections by flagging the faultsfor a user.